Design and Dynamical Investigation of a Novel 10D Hyperchaotic System with Five Positive Lyapunov Exponents

الملخص

This paper introduces a novel ten-dimensional (10D) hyperchaotic system, conceived as a high-dimensional extension of the classical Lorenz system. To attain hitherto unheard-of dynamical complexity unprecedented, the suggested system is designed with extra state variables and selective nonlinear couplings. Five positive Lyapunov exponents 

( ), a rare characteristic that denotes greater unpredictability and sensitivity, are used to establish the system's hyperchaotic nature through rigorous numerical analysis. The system's advanced nature is quantitatively confirmed by key complexity metrics, such as a Kolmogorov-Sinai entropy of 1.93 bits/iteration and a Kaplan-Yorke dimension of roughly 7.32. In terms of the number of positive Lyapunov exponents, attractor dimensionality, and entropy rate, a thorough comparison analysis demonstrates its superiority over benchmark chaotic and hyperchaotic systems such as Lorenz, Chen, and Rössler. Furthermore, the system also exhibits a wide basin of attraction, robust performance across various numerical solvers, and structural stability against parameter variations of up to ±5%. These characteristics, along with its high-dimensional phase space, make the proposed system a highly suitable candidate for cutting-edge applications, where high complexity and dependability are crucial, such as secure communication, cryptography, and chaos-based encryption